arXiv subjects

Oron Y. Propp

Publications and source records attributed to Oron Y. Propp.

3 recordsLinked to original sources

arXiv2026

Cohomological boundedness of twisted coherent Springer sheaves

We prove that the coherent Springer sheaf and its parabolic analogues are concentrated in cohomological degree $0$, as predicted by Ben-Zvi-Chen-Helm-Nadler, Zhu, Emerton-Gee-Hellmann, Hansen, and others. More generally, we show that the universal trace functor for a mixed partial affine Hecke category is right t-exact with respect to the exotic t-structure given by Bezrukavnikov-Mirković's noncommutative Springer resolution, and left t-exact with respect to the monoidally dual t-structure. To this end, we construct an explicit complex computing the universal trace functor for certain monoidal categories over quotient stacks.

math.RT↗

arXiv2019

Constructing explicit K3 spectra

Following an overview of the relevant theory, we construct several explicit examples of height-3 K3 spectra.

math.AT↗

arXiv2017

Cartan images and $\ell$-torsion points of elliptic curves with rational $j$-invariant

Let $\ell$ be an odd prime and $d$ a positive integer. We determine when there exists a degree-$d$ number field $K$ and an elliptic curve $E/K$ with $j(E)\in\mathbb{Q}\setminus\{0,1728\}$ for which $E(K)_{\mathrm{tors}}$ contains a point of order $\ell$. We also determine when there exists such a pair $(K,E)$ for which the image of the associated mod-$\ell$ Galois representation is contained in a Cartan subgroup or its normalizer, conditionally on a conjecture of Sutherland. We do the same under the stronger assumption that $E$ is defined over $\mathbb{Q}$.

math.NT↗